Modelling The Effects Of Obstacles On Dense GasDispersion In Shallow Layer Models

Abstract

A newly developed 2-d shallow layer model for dense gas dispersion in obstructed terrain is presented. The model solves the conservation equations of longitudinal and lateral momentum, dense gas mass and total mixture mass, averaged over the cloud height. Turbulence and diffusion are modelled by means of the entrainment velocity concept. The entrainment velocities are dependent on the ambient flow field and on the local cloud velocity. For model validation the Thorney Island 21 release was selected. In this field test 2000 nf of a mixture of Freon and Nitrogen with a relative density of 2 were instantaneously released. A semicircular fence 5 m high obstructed the flow 50 m from the release position. The model results are compared against the experimental in terms of the concentration time series, obtained in several positions upwind and downwind the obstacle. It is found that the predicted concentration time histories downwind the fence are in good agreement with the experiment both in the arrival time and in the order of magnitude for the sensors located on the fence axis of symmetry. Far from this axis the model underpredicts the cloud spreading. Introduction A two-dimensional shallow layer model has been developed based on the 1-d shallow layer model DISPLAY-1 [2] and on the full 3-d model ADREA-HF [1]. For the validation of the developed model the field experiment Thorney Island No. 21 has been chosen for simulation. The Thorney Island Heavy Gas Dispersion Trials (HGDT) were organised by the Health and Safety Executive (HSE, UK) in the framework of a research Transactions on Ecology and the Environment vol 6, © 1995 WIT Press, www.witpress.com, ISSN 1743-3541 1 42 Air Pollution Theory and Simulation program on the atmospheric dispersion of denser than air gases. Detailed information about the trials is given by McQuaid and Roebuck [4], The primary objective of the trials was the acquisition of reliable data at large scale in order to validate mathematical and wind tunnel models for dense gas dispersion. The experiments of phase-II (10 trials) refer to fixed volume isothermal releases under the presence of several kinds of obstructions. In trial number 21 an impermeable semicircular fence was placed around the gas source. The latter was a cylindrical container with lateral sides made of flexible plastic material. The container was placed at the centre of the semicircular fence and was filled with a mixture of Freon-12 and nitrogen with a relative (to air) density of 2.02. The ambient wind velocity was 3.9 m/sec at 10 m height. At time 0 the container collapsed rapidly to the ground leaving the gas cylinder standing instantly still. Trial 21 was chosen for simulation as in [2] and [3] because according to McQuaid and Roebuck it was fully successful and the interaction of the cloud with the fence was strong due to the relatively low wind speed. The mathematical formulation Cloud and ground surfaces We assume that the cloud surface (top) is described by a function of the form z=ht(x,y,t) and that the ground surface (bottom) by a function of the form z=hb(x,y,t), where x and y are the longitudinal and lateral coordinates in our horizontal co-ordinate system. The cloud height is: /z(%, f) = /zX%,);,r)-/2, (% ) (1) For the cloud surface the vertical component of the normal unit vector is: The conservation equations The conservation differential equations for the mixture mass, dense gas mass, x and y momentum integrated in the vertical direction over the cloud height are given below. Mixture mass equation: M + v(pM7) = p.I/.,/«,, (3) Transactions on Ecology and the Environment vol 6, © 1995 WIT Press, www.witpress.com, ISSN 1743-3541 Air Pollution Theory and Simulation 143 Dense gas mass fraction equation: